|Course Title||Code||Semester||L+P Hour||Credits||ECTS|
|Complex Analysis *||MT 433||7||3||3||5|
|Prerequisites and co-requisites|
|Recommended Optional Programme Components||None|
|Language of Instruction||Turkish|
|Course Level||First Cycle Programmes (Bachelor's Degree)|
|Course Coordinator||Assoc.Prof.Dr. Nazar Şahin ÖĞÜŞLÜ|
Calculate certain integrals of some special types of complex functions, write and prove that the sum of series formulas, find the sum of the series, explain the relationship between zeros and poles of a complex function in an area, find the number of zeros and poles of a complex function in an area, decide whether a function conformal and can apply on curves, explain the relationship between the convergence of an infinite multiplication with convergence of an infinite series, calculate some of the infinite multiplication.
Integrals, sum of series, poles and zeros, conformal mappings, infinite multiplication
|Course's Contribution To Program|
|No||Program Learning Outcomes||Contribution|
Is able to prove Mathematical facts encountered in secondary school.
Recognizes the importance of basic notions in Algebra, Analysis and Topology
Develops maturity of mathematical reasoning and writes and develops mathematical proofs.
Is able to express basic theories of mathematics properly and correctly both written and verbally
Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines.
Expresses clearly the relationship between objects while constructing a model
Draws mathematical models such as formulas, graphs and tables and explains them
Is able to mathematically reorganize, analyze and model problems encountered.
Knows at least one computer programming language
Uses effective scientific methods and appropriate technologies to solve problems
Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians
In addition to professional skills, the student improves his/her skills in other areas of his/her choice such as in scientific, cultural, artistic and social fields
Knows programming techniques and is able to write a computer program
Is able to do mathematics both individually and in a group.
|1||General information, derivative, Cauchy-Riemann equations, analytic functions, Cauchy-Gaursat theorem, series and residual calculations, brief review.||Review of the relevant pages from sources|
|2||Integrals||Review of the relevant pages from sources|
|3||Calculation of definite integrals contaning sine and cosine expressions.||Review of the relevant pages from sources|
|4||Definite integrals of multi-valued functions.||Review of the relevant pages from sources|
|5||Cauchy principal value and trigonometric integrals.||Review of the relevant pages from sources|
|6||Proof of formulas of the sum of series.||Review of the relevant pages from sources|
|7||Applications related to the calculation of the sum of series.||Review of the relevant pages from sources|
|8||Written exam||topics discussed in the lecture notes and sources again|
|9||Mittag-Lefflers theorem, proof and applications.||Review of the relevant pages from sources|
|10||Proof of formulas related to the relationship between zeros and poles and its applications.||Review of the relevant pages from sources|
|11||Rouche theorem and its applications.||Review of the relevant pages from sources|
|12||Conformal mappings.||Review of the relevant pages from sources|
|13||Applications related to conformal mappings||Review of the relevant pages from sources|
|14||Definition and properties of infinite products.||Review of the relevant pages from sources|
|15||Some applications related to infinite products.||Review of the relevant pages from sources|
|16-17||Final exam||topics discussed in the lecture notes and sources again|
|Recommended or Required Reading|
|Textbook||COMPLEX VARIABLES AND APPLICATIONS, Authors: Ruel V. Churchill, James Ward Brown|
KOMPLEKS FONKSİYONLAR TEORİSİ, Yazar: Prof.Dr. Turgut Başkan
KARMAŞIK FONKSİYONLAR KURAMI, Yazar: Prof.Dr. Ali Dönmez